ar X iv : m at h . A G / 0 51 01 26 v 2 5 N ov 2 00 5 TROPICAL DISCRIMINANTS
نویسندگان
چکیده
Tropical geometry is used to develop a new approach to the theory of discriminants and resultants in the sense of Gel'fand, Kapranov and Zelevinsky. The tropical A-discriminant, which is the tropicalization of the dual variety of the projective toric variety given by an integer matrix A, is shown to coincide with the Minkowski sum of the row space of A and the tropicalization of the kernel of A. This leads to an explicit positive formula for the extreme monomials of any A-discriminant, and to a combinatorial rule for deciding when two regular triangulations of A correspond to the same monomial of the A-discriminant.
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تاریخ انتشار 2007